(dy/dx)sin x=yln y的通解

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/24 11:43:32
(dy/dx)sin x=yln y的通解
xj@_e&鲞^!MB*]CQ'AmB{`|1~ dog$I/$$t_?UsFDHr-P$4'PUC Z%*)' ā` Jf=9-'YwqxGn9ތbKV#~]i DD* 3G^ * Z;*Q3G3Y d aB5eIcCY%fy Zil_hǬ>g7cK8xakGi!25G}0Ta9!LJ ( Hn10WmV+)+Jz& ,~y

(dy/dx)sin x=yln y的通解
(dy/dx)sin x=yln y的通解

(dy/dx)sin x=yln y的通解
∫1/y*1/lny dy=∫1/sinx dx
lnlny=∫1/2/[sin(x/2)*cos(x/2)] dx
lnlny=ln(sin(x/2))-ln(cos(x/2))+c
lny=e^c*tan(x/2) 这里e^c写作C,因为毕竟还是常数.
y=e^(C*tan(x/2))

(dy/dx)sinx=ylny d(lny)/lny=sinxdx/[1-(cosx)^2]
ln[ln(y)]=-dcosx/[(1-cosx)(1+cosx)] ln[ln(y)]=(-1/2)[dcosx/(1-cosx)+dcosx/(1+cosx)]
ln[ln(y)=-ln√[(1-cosx)/(1+cosx)]+C
ln[(lny)]=lntg(x/2)+C

分离变量，dy/(yln y)=dx/sin x,∫dy/(yln y)= ∫ dx/sin x ，
∫dlny/ln y= ∫ cscxdx,ln(lny)=ln|cscx-cotx|+C1=ln|tan(x/2)|+C1,
(lny)=e^[ln|tan(x/2)|+C1],y=e^[e^(C1)|tan(x/2)|]=e^[Ctan(x/2)]

(dy/dx)sin x=yln y的通解 隐函数x=yln(y)d的微分dy dy/dx=y/(sin(y)-x) 的积分 隐函数x=yln(xy)的微分dy xdy/dx=yln(y/x)的通解齐次方程 微分方程(x+y)(dx-dy)=dx+dy的通解 d{cos(x-y)=sin(x-y)(dx-dy)这里dx-dy是什么意思呢? 求xdy/dx=ylny/x的微分方程通解正确的是xdy/dx=yln(y/x) x=sin(y/x)+e^2 求dy/dx y=sin(x^2),dy/dx=? 设sin(x+y)=xy,求dy/dx. 求通解dy/dx=sin(x-y) y = sin²（x²）求 dy / dx 求微分方程x*dy/dx+x+sin(x+y)=0的通解 求dy/dx+y/x=x/sin x 的微分方程 微分方程x(dy/dx)=y+x^2 sin x的通解是 y=[sin(x^4)]^2,则dy/dx=?,dy^2/dx^2=?,dy/d(x^2)=? dy/dx=-y/x 的通解